Many authors have taken up the challenge of formulating physicalism as a supervenience thesis. These endeavors have met with varying response, but it seems that the general consensus still remains that a supervenience thesis that is both sufficient and necessary for physicalism has yet to be developed. Terence Horgan1 and Jaegwon Kim2 have most famously argued that supervenience theses are not sufficiently strong for physicalism. Nonetheless, several recent articles suggest that there are philosophers who still hold out hope for some type of supervenience of the mental upon the physical being, if not both sufficient and necessary, at least necessary for physicalism.3 In this paper, I will 1) investigate some of the motivation for finding a supervenience thesis that characterizes physicalism, 2) briefly review the types of supervenience theses that have been proposed as necessary (or necessary and sufficient) for physicalism, and 3) investigate in some detail the recent supervenience thesis proposed by Frank Jackson and expounded upon by Gene Witmer. Jackson, in his recent book, claims to have a supervenience thesis that is both necessary and sufficient for physicalism